Logs are pretty good for lying down in mud or very small streams to allow other vehicles to pass over without getting stuck. You used to see a bunch of them in WWII:

Edit: However, if I was in that BMP, I wouldn't complain about the small extra protection they might provide.

Some missiles have two charges. One explodes on the outside of the tank to get rid of the active armor and the second penetrates the hull then. When using a layer of wood, probably the first one detonates at the wood, second on reactive armor and hull stays intact.